In many election cycles, there’s a snappy shorthand used to describe the type of voters who may help decide the winner. Think soccer moms or security moms. Even Nascar dads. For 2024, it’s the “mama bears.”

These conservative mothers and grandmothers, who in recent years have organized for parental rights, including limiting discussion of radical gender ideology in schools, have been classified as extremists by a liberal advocacy group, the Southern Poverty Law Center. They have also been among the most coveted voters so far in the 2024 Republican presidential primary.

President Trump praised their work, saying organizations such as Moms for Liberty had taught the liberal left a lesson: “Don’t mess with America’s moms.” Governor DeSantis said “woke” policies had “awakened the most powerful political force in the country: mama bears.” His wife, Casey DeSantis, who launched “Mamas for DeSantis” in leadoff-voting Iowa, said mothers and grandmothers were the “game changer” in Mr. DeSantis’s blowout win for a second term as Florida governor. She predicted they will be again as he runs for president.

“We saw there was a constituency of folks who really wanted a voice, and it wasn’t just Republicans. It was independents, but also a lot of Democrats, too, who didn’t like the direction that the country was going,” Mrs. DeSantis said during a talk peppered with stories about raising children in the governor’s mansion, with slime on the ceiling and crayon on wallpaper.

“It’s one thing when your policies come after us as mamas,” she said. “It’s another thing when your policies come after our children, and that’s when the claws come out.”

These so-called mama bears whom Mr. DeSantis and other Republicans are courting are conservative women living across America. They may belong to official groups such as Moms for Liberty, which says it has 120,000 members nationally, or smaller ones like No Left Turn in Education. Some belong to no group at all.

The groups and their work took off during the Covid pandemic, when they say parents got a closer look at what their children were being exposed to in public schools. They grew in numbers after President Biden defeated Mr. Trump in 2020 and were motivated by what they called government overreach and “woke” policies.

Many fought pandemic-related school shutdowns and mask mandates, pushed to remove diversity, equity and inclusion programs from schools and tried to ban books they viewed as inappropriate, such as ones with sexually explicit LGBTQ content. They have turned up en masse at school board and library board meetings, fighting to ban instruction on gender identity and sexual orientation. They have run school board candidates who support their stances.

Geralyn Jones, 31, of Marion, Iowa, said she was not active in politics until the pandemic, when she grew concerned about mask requirements and online schooling for her son, who was in kindergarten. She started asking questions and did not like the answers she was getting.

Ms. Jones pulled her two kids out of public school after the district approved a policy that allows transgender students to use the bathroom or locker room of the gender they identify as, without alerting parents. She now leads the Linn County chapter of Moms for Liberty and said that seeing other moms get involved in politics is empowering.

Ms. Jones, who voted for Mr. Trump in 2016 and 2020, says he and many other 2024 candidates have reached out to Moms for Liberty — not the other way around — to schedule time to meet with moms. They arrange roundtables for the candidates and always exceed the number of spots the Trump campaign reserves for their group at special events.

“I think we are going to be the most sought-out group or sought-out voice in this next election,” she said.

At the Mamas for DeSantis event, there were games for children who came with their parents. Attendees held little ones on their laps. The DeSantis campaign also has started selling “Mamas for DeSantis” T-shirts and tote bags.

Opponents say the warm-fuzzy image of a mama bear is a way to mask what she said was an extreme agenda.

“Republicans have decided that this is, I think, their golden ticket for the primaries to rile up their base,” Katie Paris, who runs Red, Wine and Blue, a network of women pushing back on the efforts of Moms for Liberty, said.

“Call it parents rights, call it mama bears, and try to make it sound like something that would be common sense,” Ms. Paris said. “The reality about parents’ rights is that it’s just about the rights of a vocal minority that is trying to carry out an extreme political agenda.”

The mama bear movement is “a contemporary iteration of a trend we’ve seen before” and that dates back decades, a professor at Point Loma Nazarene University, Linda Beail, who wrote a book about Sarah Palin, the 2008 Republican vice presidential nominee, said.

Ms. Palin was a game changer in many ways — a youngish, attractive, and successful woman who also was quite conservative, Ms. Beail said. In the 2010 midterms, Ms. Palin used the phrase “mama grizzlies” to describe the conservative women she said would stop Democrats. The narrative played to ideas of rugged individualism, especially appealing in rural areas, and portrayed women as fiercely protective, defending a traditional way of life and motivated by their children.

“It’s hard to argue with,” Ms. Beail said. “It’s selflessly protecting your cubs, right?”

In 2024, being a mama bear also may provide a space for conservative women who have not been politically active before or who may have sat out previous elections. If the mama bear narrative is persuasive, Ms. Beail said, there are a lot of women who could say, “That’s the spot for me.”

In 2020, women supported Mr. Biden over Mr. Trump 55 percent to 43 percent, while men supported Mr. Trump over Mr. Biden 51 percent to 46 percent. There was little difference between mothers of children under 18 and women overall in how they voted either year.

Ms. Jones, the Iowa mother, defended the work that Moms for Liberty and other groups are doing, saying they are getting backlash for simply trying to protect their children. She says the criticism is evidence of the momentum behind their movement and that lawmakers and candidates are talking more about education than she has ever seen — one more sign of how important mothers will be in 2024.

“There’s a mom in every household for the most part,” she said, “so that’s a voice that definitely carries a lot of weight.”